Modeling Heat Conduction in Spiral Geometries

The spirally wound design is of importance to battery manufacturers as it improves the energy and power densities, by using lesser accessories when compared with the prismatic design. 1-2 For this reason, the spirally-wound design is used in a variety of battery systems ~e.g., Li-SOCl2 , 3 Li bromine chloride complexing additive ~BCX!, 4 lead-acid, 5 Zn-MnO2 , 6 Li-ion 1-2,7 !. However, because of their lower surface area to volume ratio, spiral batteries retain more heat than prismatic batteries. Therefore, in order to improve thermal management and achieve safe operation of large-scale spirally wound batteries, it is important to understand their thermal behavior, especially during high rate operation. A cost effective method of studying heat transport during the operation of a battery is to theoretically simulate the temperatures attained by the battery. However, very few publications 3-9 exist in the literature that couple electrochemical and thermal behavior in spirally wound batteries. Rather, most thermal models of spirally wound batteries estimate the heat generation rate a priori from experimental voltage-time data. 3-4,7-9 Cho and Halpert 8 and Cho 9 assumed that the entire battery operates at a uniform temperature, while Al Hallaj et al. 7 simulated a 1-D radial variation in temperature. Evans and White 3 and Kalu and White 4 accounted for both radial and spiral heat conductions in their spirally wound battery systems using a two-dimensional ~2-D! model for the energy balance. Evans and White 3 compared the predictions of the 2-D model